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Question

Given tan(A+B)=3 and tan(AB)=13

If B<A<90, then,
A (in degrees) = ___
B (in degrees) = ___

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Solution

Given
tan(A+B)=3

Now we know that tan 60=3

A+B=60 ------------------- (1)

tan(AB)=13

Now we know that tan 30=13

AB=30 --------------------- (2)

Adding equations 1 and 2, we get

2A=90

A=45

Subtracting 2 from 1, we get

2B=30

B=15

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